Basra's climate is extreme. Summers (June–September) are brutally hot — regularly above 50°C — and almost impossible for comfortable sightseeing. The winter months, November through March, are by far the best time to visit: temperatures drop to a pleasant 15–25°C, skies are clear, and the city is at its most liveable.
Spring (April–May) can be pleasant before the heat arrives. Autumn (October–November) is transitional and also manageable. Ramadan changes the rhythm of the city significantly — many restaurants and shops are closed during daylight hours, though the evenings come alive.
The religious calendar matters here. Ashura, the Shia commemoration marking the death of Imam Hussein at Karbala, draws enormous processions to Basra's mosques and streets. It is a powerful spectacle if you can travel safely and respectfully, but the city is enormously crowded and emotions run high. Check the Islamic calendar for dates, which shift each year.